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Math Problems
Algebra 2
Csc, sec, and cot of special angles
Express the radical using the imaginary unit,
i
i
i
. Express your answer in simplified form.
\newline
±
−
22
=
±
\pm \sqrt{-22} = \pm
±
−
22
=
±
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Express the radical using the imaginary unit,
i
i
i
. Express your answer in simplified form.
\newline
±
−
22
=
±
\pm \sqrt{-22} = \pm
±
−
22
=
±
Get tutor help
Rewrite the expression in the form
b
n
b^n
b
n
.
\newline
b
4
×
b
−
1
4
=
b^4 \times b^{-\frac{1}{4}} =
b
4
×
b
−
4
1
=
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y
2
+
25
=
x
10
y
=
x
\begin{aligned} y^2+25&=x \ 10y&=x \end{aligned}
y
2
+
25
=
x
10
y
=
x
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question:
2
x
⋅
4
x
−
i
n
y
5
2
2\sqrt{x}\cdot 4x^{^{^{- iny\dfrac{5}{2}}}}
2
x
⋅
4
x
−
in
y
2
5
=
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Heron's Formula: Unit test
\newline
The area of the triangle with sides
11
c
m
,
9
c
m
11 \mathrm{~cm}, 9 \mathrm{~cm}
11
cm
,
9
cm
and
12
c
m
12 \mathrm{~cm}
12
cm
is of the form
y
35
c
m
2
y \sqrt{35} \mathrm{~cm}^{2}
y
35
cm
2
.
\newline
Find the value of
y
y
y
.
\newline
□
\square
□
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Heron's Formula: Unit test
\newline
The area of the triangle with sides
11
c
m
,
9
c
m
11 \mathrm{~cm}, 9 \mathrm{~cm}
11
cm
,
9
cm
and
12
c
m
12 \mathrm{~cm}
12
cm
is of the form
y
35
c
m
2
y \sqrt{35} \mathrm{~cm}^{2}
y
35
cm
2
.
\newline
Find the value of
y
y
y
.
\newline
□
\square
□
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d
d
x
(
2
x
+
3
(
x
−
4
)
2
)
=
\frac{d}{dx}\left(\frac{2x+3}{(x-4)^{2}}\right)=
d
x
d
(
(
x
−
4
)
2
2
x
+
3
)
=
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Simplify.
\newline
Remove all perfect squares from inside the square roots. Assume
\newline
x
x
x
and
\newline
z
z
z
are positive.
\newline
72
x
3
z
3
=
□
\sqrt{72x^{3}z^{3}}=\square
72
x
3
z
3
=
□
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(
sin
x
+
sinh
x
)
d
x
(\sin x+\sinh x) d x
(
sin
x
+
sinh
x
)
d
x
=
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If
x
2
−
a
=
(
x
−
3
)
(
x
+
3
)
x^{2}-a=(x-3)(x+3)
x
2
−
a
=
(
x
−
3
)
(
x
+
3
)
, then
a
=
a=
a
=
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If
x
2
−
y
2
=
x
+
y
x^{2}-y^{2}=x+y
x
2
−
y
2
=
x
+
y
, then
x
−
y
=
x-y=
x
−
y
=
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Simplifying the Expression:
2
π
J
(
1
+
(
e
−
J
3
)
)
=
2\pi J\left(1+\left(\frac{e^{-J}}{3}\right)\right)=
2
π
J
(
1
+
(
3
e
−
J
)
)
=
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d
y
d
x
=
1
x
\frac{d y}{d x}=\frac{1}{x}
d
x
d
y
=
x
1
and
y
(
e
)
=
−
2
y(e)=-2
y
(
e
)
=
−
2
.
\newline
y
(
e
3
)
=
y\left(e^{3}\right)=
y
(
e
3
)
=
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Let
y
=
x
e
x
y=\sqrt{x} e^{x}
y
=
x
e
x
.
\newline
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
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d
d
x
[
cos
(
x
)
x
2
]
=
\frac{d}{d x}\left[\cos (x) x^{2}\right]=
d
x
d
[
cos
(
x
)
x
2
]
=
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d
d
x
(
e
x
cos
(
x
)
)
=
\frac{d}{d x}\left(e^{x} \cos (x)\right)=
d
x
d
(
e
x
cos
(
x
)
)
=
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If
2
a
=
2
4
9
2^{a}=\sqrt[9]{2^{4}}
2
a
=
9
2
4
, what is the value of
a
a
a
?
\newline
◻
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Distribute to create an equivalent expression with the fewest symbols possible.
1
2
(
10
x
+
20
y
+
10
z
)
=
\dfrac{1}{2}(10x + 20y +10z) =
2
1
(
10
x
+
20
y
+
10
z
)
=
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Distribute to create an equivalent expression with the fewest symbols possible.
1
2
(
10
x
+
20
y
+
10
z
)
=
\dfrac{1}{2}(10x + 20y +10z) =
2
1
(
10
x
+
20
y
+
10
z
)
=
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lim
θ
→
0
+
(
sin
(
π
−
θ
)
)
θ
\lim _{\theta \rightarrow 0^{+}}(\sin (\pi-\theta))^{\theta}
lim
θ
→
0
+
(
sin
(
π
−
θ
)
)
θ
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∫
x
arcsin
x
d
x
=
\int x \arcsin x d x=
∫
x
arcsin
x
d
x
=
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(x)
lim
x
→
+
∞
x
x
+
1
=
\lim _{x \rightarrow+\infty} \frac{\sqrt{x}}{x+1}=
lim
x
→
+
∞
x
+
1
x
=
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Evaluate. Write your answer as a whole number or as a simplified fraction.
\newline
5
5
5
2
=
\frac{5^{5}}{5^{2}}=
5
2
5
5
=
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Find all angles,
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
, that solve the following equation.
\newline
sin
θ
=
0
\sin \theta=0
sin
θ
=
0
\newline
Answer:
θ
=
\theta=
θ
=
Get tutor help
Find all angles,
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
, that solve the following equation.
\newline
sin
θ
=
3
2
\sin \theta=\frac{\sqrt{3}}{2}
sin
θ
=
2
3
\newline
Answer:
θ
=
\theta=
θ
=
Get tutor help
Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form.
\newline
40
x
3
36
x
2
\frac{40 x^{3}}{36 x^{2}}
36
x
2
40
x
3
\newline
Answer:
Get tutor help
Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form.
\newline
14
x
8
x
\frac{14 x}{8 x}
8
x
14
x
\newline
Answer:
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Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form.
\newline
84
x
96
x
\frac{84 x}{96 x}
96
x
84
x
\newline
Answer:
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Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form.
\newline
12
x
4
5
x
2
\frac{12 x^{4}}{5 x^{2}}
5
x
2
12
x
4
\newline
Answer:
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Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form.
\newline
9
x
2
81
x
4
\frac{9 x^{2}}{81 x^{4}}
81
x
4
9
x
2
\newline
Answer:
Get tutor help
Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form.
\newline
60
x
3
72
x
2
\frac{60 x^{3}}{72 x^{2}}
72
x
2
60
x
3
\newline
Answer:
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Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form.
\newline
14
x
3
21
x
4
\frac{14 x^{3}}{21 x^{4}}
21
x
4
14
x
3
\newline
Answer:
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Perform the operation and express your answer as a single fraction in simplest form.
\newline
5
x
+
1
4
x
2
5 x+\frac{1}{4 x^{2}}
5
x
+
4
x
2
1
\newline
Answer:
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Perform the operation and express your answer as a single fraction in simplest form.
\newline
5
3
x
2
−
4
15
x
3
\frac{5}{3 x^{2}}-\frac{4}{15 x^{3}}
3
x
2
5
−
15
x
3
4
\newline
Answer:
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Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form.
\newline
35
x
2
2
\frac{35 x^{2}}{2}
2
35
x
2
\newline
Answer:
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Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form.
\newline
48
88
x
4
\frac{48}{88 x^{4}}
88
x
4
48
\newline
Answer:
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Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form.
\newline
7
x
5
x
\frac{7 x}{5 x}
5
x
7
x
\newline
Answer:
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Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form.
\newline
22
x
55
x
4
\frac{22 x}{55 x^{4}}
55
x
4
22
x
\newline
Answer:
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Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form.
\newline
33
x
2
37
\frac{33 x^{2}}{37}
37
33
x
2
\newline
Answer:
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Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form.
\newline
40
x
3
12
x
4
\frac{40 x^{3}}{12 x^{4}}
12
x
4
40
x
3
\newline
Answer:
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Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form.
\newline
32
x
44
x
2
\frac{32 x}{44 x^{2}}
44
x
2
32
x
\newline
Answer:
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Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form.
\newline
60
x
2
35
x
\frac{60 x^{2}}{35 x}
35
x
60
x
2
\newline
Answer:
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Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form.
\newline
36
33
x
2
\frac{36}{33 x^{2}}
33
x
2
36
\newline
Answer:
Get tutor help
Find all angles,
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
, that satisfy the equation below, to the nearest tenth of a degree.
\newline
4
cos
2
θ
=
4
cos
θ
−
1
4 \cos ^{2} \theta=4 \cos \theta-1
4
cos
2
θ
=
4
cos
θ
−
1
\newline
Answer:
θ
=
\theta=
θ
=
Get tutor help
Find all angles,
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
, that satisfy the equation below, to the nearest tenth of a degree.
\newline
−
6
sin
2
θ
−
9
=
7
sin
θ
−
8
-6 \sin ^{2} \theta-9=7 \sin \theta-8
−
6
sin
2
θ
−
9
=
7
sin
θ
−
8
\newline
Answer:
θ
=
\theta=
θ
=
Get tutor help
Find all angles,
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
, that satisfy the equation below, to the nearest tenth of a degree.
\newline
8
sin
2
θ
+
6
sin
θ
=
−
1
8 \sin ^{2} \theta+6 \sin \theta=-1
8
sin
2
θ
+
6
sin
θ
=
−
1
\newline
Answer:
θ
=
\theta=
θ
=
Get tutor help
Find all angles,
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
, that satisfy the equation below, to the nearest tenth of a degree.
\newline
6
tan
2
θ
=
11
tan
θ
+
7
6 \tan ^{2} \theta=11 \tan \theta+7
6
tan
2
θ
=
11
tan
θ
+
7
\newline
Answer:
θ
=
\theta=
θ
=
Get tutor help
Find all angles,
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
, that satisfy the equation below, to the nearest tenth of a degree.
\newline
4
sin
2
θ
+
sin
θ
=
0
4 \sin ^{2} \theta+\sin \theta=0
4
sin
2
θ
+
sin
θ
=
0
\newline
Answer:
θ
=
\theta=
θ
=
Get tutor help
Find all angles,
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
, that satisfy the equation below, to the nearest tenth of a degree.
\newline
sin
2
θ
−
8
sin
θ
+
12
=
0
\sin ^{2} \theta-8 \sin \theta+12=0
sin
2
θ
−
8
sin
θ
+
12
=
0
\newline
Answer:
θ
=
\theta=
θ
=
Get tutor help
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